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Invariant almost Hermitian structures on flag manifolds
Abstract Let G be a complex semi-simple Lie group and form its maximal flag manifold F =G/P=U/T where P is a minimal parabolic (Borel) subgroup, U a compact real form and T=U∩P a maximal torus of U.Expand
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Semiflows on Topological Spaces: Chain Transitivity and Semigroups
This paper studies semiflows on topological spaces. A concept of chain recurrence, based on families of coverings, is introduced and related to Morse decomposition. The chain transitive componentsExpand
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Invariant control sets on flag manifolds
  • L. S. Martin
  • Mathematics, Computer Science
  • Math. Control. Signals Syst.
  • 1 March 1993
TLDR
We study invariant control sets for the action of S on homogeneous spaces of a semisimple Lie group on the boundary manifolds of the group. Expand
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A multiplicative ergodic theorem for rotation numbers
Given a vector fieldX on a Riemannian manifoldM of dimension at least 2 whose flow leaves a probability measureμ invariant, the multiplicative ergodic theorem tells us thatμ-a.s. every tangent vectorExpand
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Maximal semigroups in semi-simple Lie groups
The maximal semigroups with nonempty interior in a semi-simple Lie group with finite' center are characterized as compression semigroups of subsets in the flag manifolds of the group. For thisExpand
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Controllability properties of a class of control systems on lie groups
Linear control systems on Lie groups were introduced by Markus [3] and also studied by Ayala and Tirao in [1]. For this class of control systems we establish controllability results in the compactExpand
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Morse and Lyapunov spectra and dynamics on flag bundles
Abstract In this paper we study characteristic exponents of flows in relation with the dynamics of flows on flag bundles. The starting point is a flow on a principal bundle with semi-simple group G.Expand
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On global controllability of discrete-time control systems
  • L. S. Martin
  • Mathematics, Computer Science
  • Math. Control. Signals Syst.
  • 1 September 1995
TLDR
This paper gives sufficient conditions for global controllability of a discrete-time control system which is obtained by discretizing a continuous-time bilinear system. Expand
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Controllability of two-dimensional bilinear systems
For bilincar control systems x = Ax + uBx, x ∊ R2 , A and B 2 x 2 matrices, necessary and sufficient conditions are given for the controllability on R2 -{0}. The method is through Lie theory, andExpand
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Covering space for monotonic homotopy of trajectories of control systems
Abstract This paper considers monotonic (or causal) homotopy between trajectories of control systems. The main result is the construction of an analogue of the simply connected covering space. TheExpand
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